One of the more important statistical tools for the monitoring and analysis of the economic activity evolution in the short term is the availability of estimations of the quarterly GDP components, whether the supply side or whetherthe demand side. The need for having this information with a short lag, makes itessential the use of quarterly distribution methods that allow distribute the annualinformation to quarter.The more applied tool, due to the fact that it allows to solve this problem in a very graceful way under an statistic point of view of optimal estimator, is the Chow-Lin method. Nevertheless, this method do not guarantee the coincidencebetween the GDP quarterly estimations by the supply side and the demand side.This leads to the need of a conciliation method.In this paper it is developed a multivariate extension of the Chow-Lin method that allows to solve the quarterly values estimation problem in an optimal way, subject to several restrictions. One of the potential applications of thismethod, that we have named the restricted Chow-Lin method, is the joint estimation of quarterly side, conditioned to the need that both GDP estimations have to be equal, avoiding the need of applying further conciliation methods.